Can one sum all Feynman diagrams
for the unitary Fermi gas?
R. Rossi, K. Van Houcke, F. Werner
ENS Paris
T. Ohgoe
University of Tokyo
E. Kozik
King's College, London
N. Prokof'ev, B. Svistunov
University of Massachusetts, Amherst
sum all diagrams up to order ~9
using Diagrammatic Monte Carlo
Fully dressed pair propagator:
Bold Diagrammatic
Monte Carlo
10^5
10^5
Resummation of divergent series
Diagrammatic series:
(where
Lindelöf resummation:
underlying logic: Euler's principle
sum of all diagrams of order n)
assuming non-zero radius of convergence
Lindelöf resummation:
assuming non-zero radius of convergence
[Van Houcke, Werner, Kozik, Prokof'ev, Svistunov,
Ku, Sommer, Cheuk, Schirotzek, Zwierlein,
Nature Phys. 2012]
but ...
but ...
radius of convergence is zero
Borel resummation:
in practice:
can work even for
zero radius of convergence
Can we design more powerful resummation methods?
How do we know that radius of convergence is zero?
Large-order asymptotics
(PhD of R. Rossi - work in progress)
[Van Houcke et al., arXiv 2013]